Kerry Back
A financial option is a right to buy or sell a financial security.
The right trades separately from the (underlying) security and usually even on a different exchange.
The rights are not (usually) issued by the companies who issue the underlying securities.
A call option is the right to buy an asset at a pre-specified price.
A put option is the right to sell an asset at a pre-specified price.
The pre-specified price is called the exercise price or strike price.
Borrowing language from horse racing, we say a call is
The reverse for puts
Also, “deep in the money” and “deep out of the money”
\[\begin{cases} 0 & \text{if underlying < strike}\\ \text{underlying} - \text{strike} & \text{if underlying > strike} \end{cases} \]
\[\max(\text{underlying price}-\text{strike}, 0)\]
With strike = 50,
\[\begin{cases} \text{strike} - \text{underlying} & \text{if underlying < strike}\\ 0 & \text{if underlying > strike} \end{cases} \]
\[\max(\text{strike}-\text{underlying price}, 0)\]
With strike = 50,